The idea behind distillation is quite simple to understand. Given a mixture of two miscible liquids, if they have very disparate boiling points, we should be able to heat up the mixture to a temperature that is above the boiling point of one compound, but below the boiling of the other. This will cause the one with the lower boiling point to go into the gas phase, such that we can collect the vapor and condense it elsewhere, while the one with the higher boiling will just stay right where it is.